Ferrimagnetic resonance relaxation in rare-earth iron garnets

Abstract

A quantitative analysis has been made of the ferrimagnetic resonance relaxation in rare-earth iron garnets. The data considered consist of measurements of the ferrimagnetic resonance linewidth of yttrium iron garnet substituted with neodymium, samarium, dysprosium, holmium, erbium, and ytterbium taken from 4.2°K to just below the Curie point, as well as data of other investigators for terbium and thulium. The data are conveniently divided into the two groups of odd and even electron ions. The ions in each group behave in a similar manner, the only exceptions being thulium and ytterbium. It is assumed that all the relaxation occurs through the strongly relaxing rare-earth ions but we find that both the "fast relaxation" theory of de Gennes, Kittel, and Portis and the "slow relaxation" theory of Clogston, Van Vleck, and Orbach fail to provide agreement with experiment. We have, however, formulated an empirical relation containing a relaxation term of the "slow relaxation" type that provides an excellent fit to the data when one regards the relaxation of the rare earth as being the familiar one-ion spin-lattice relaxation due to the direct (one phonon) and Orbach (two phonon) processes. The observed temperature dependence of the linewidth is satisfactorily accounted for if one assumes the direct process for the odd electron ions and the Orbach process for the even electron ions. In the case of thulium, one finds it necessary to assume the direct process, and for ytterbium one finds evidence for both processes, the direct process being dominant at low temperatures and the Orbach process dominant at high temperatures. The analysis allows evaluation of the iron-rare-earth exchange frequency and the rare-earth relaxation parameters. The exchange frequencies are found to be in good agreement with the values obtained by other investigators. In the one case where independent relaxation time measurements exist, that of samarium iron garnet, the behavior we find from the linewidth measurements agrees with that found by Caspari et al. by γ-γ correlation experiments. The frequency dependence predicted by the empirical relation is also in accord with experiment and a quantitative calculation of the frequency dependence of the peak value of the linewidth and the temperature of the linewidth peak yields excellent agreement with the data of Dillon for terbium. © 1964 The American Institute of Physics.